Question

EXPRESS 5.0081 IN P/Q FORM AND BAR ON 81

Answer 1

Answer:

LET X=5.00818181......

X=5.00818181.....

10000X=50081.818181.....

10000X=50076+X

10000X-X=50076

9999X=50076

X=50076/9999

Answer 2

Answer:

$\frac{5509}{1100}$ is the P/Q form of $5.00\overline{81}$.

Step-by-step explanation:

Step 1 of 3

Consider the given number as follows:

$5.00\overline{81}$

or,

$5.00\overline{81}=5.00818181...$

Now, let $x=5.00\overline{81}$. Then,

$x=5.008181...$ . . . . . (1)

Step 2 of 3

Multiply both the sides of the equation (1) by $100$.

⇒ $100x=100\times5.008181...$

⇒ $100x=500.8181...$ . . . . . (2)

Now, multiply both the sides of the equation (1) by $10000$.

⇒ $10000x=10000\times5.008181...$

⇒ $10000x=50081.8181...$ . . . . . (3)

Step 3 of 3

Find the value of $x$.

Subtract the equation (2) from the equation (3) as follows:

⇒ $10000x-100x=50081.8181...-500.8181...$

⇒ $9900x=49581$

⇒ $x=\frac{49581}{9900}$

On simplifying, we get

$x=\frac{5509}{1100}$

Therefore, the number $5.00\overline{81}$ in P/Q form is $\frac{5509}{1100}$.

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